Linear Operators: Spectral theory |
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Page 1529
Then in this angle any solution of Lj = 0 whose asymp) zk – Lf O totic expansion begins with the factor exp ( 512k - 1 ) is exponentially small ( as z → o in the angle ) relative to any solution whose asymp. totic expansion begins with ...
Then in this angle any solution of Lj = 0 whose asymp) zk – Lf O totic expansion begins with the factor exp ( 512k - 1 ) is exponentially small ( as z → o in the angle ) relative to any solution whose asymp. totic expansion begins with ...
Page 1553
Suppose that q is bounded below on the interval [ 0 , 00 ) , and let f be a bounded solution of the equation ( 1 -- T ) ... ( b ) if all solutions of the equation ( 2-1 ) } = 0 are bounded , then I belongs to the essential spectrum of t .
Suppose that q is bounded below on the interval [ 0 , 00 ) , and let f be a bounded solution of the equation ( 1 -- T ) ... ( b ) if all solutions of the equation ( 2-1 ) } = 0 are bounded , then I belongs to the essential spectrum of t .
Page 1556
What is the relationship between 0 ( t ) and the number of zeros of a solution of the above equation ? G14 Use the result of the preceding exercise to show that if the operator t has two boundary values at infinity , then N ( t ) lim ...
What is the relationship between 0 ( t ) and the number of zeros of a solution of the above equation ? G14 Use the result of the preceding exercise to show that if the operator t has two boundary values at infinity , then N ( t ) lim ...
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Contents
8 | 876 |
859 | 885 |
extensive presentation of applications of the spectral theorem | 911 |
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additive adjoint adjoint operator algebra analytic assume basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero